What 20th century individuals think is of little consequence.
You said what individuals think doesn't matter. But you're an individual. Your understanding of what the church fathers believed might be all wrong.
What the Universal belief of the early Church was is what guides us to proper understanding of the subject. The key Scripture reference to being "born again" or "regenerated" is John 3:5, where Jesus says, "Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God." The early Christians uniformly identified this verse with baptism. Water baptism is the way, they said, that we are born again and receive new lifeâ€â€a fact that is supported elsewhere in Scripture (Rom. 6:3–4; Col. 2:12–13; Titus 3:5). No Church Father referred to John 3:5 as anything other than water baptism.
Romans 6:3-4 Paul said we were baptized into his death.
Col. 2:12-13 Paul said we were buried with him in baptism and also raised with him through faith in the working of God, who raised him from the dead. Basically he's saying we were baptized into his death and we were raised with him through faith in the working of God, referring to the resurrection.
Titus 3:5 Paul said he saved us, not because of deeds done by us, but in virtue of his own mercy, by the washing of regeneration and renewal in the Holy Spirit, which he poured out on us richly through Jesus Christ our Saviour.
Here we have Paul referring to the action of the water and the Spirit. The water is for forgiveness in the name of Jesus Christ. Like Peter said, "Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you shall receive the gift of the Holy Spirit." And the Spirit is for renewal. Jesus said, 'you must be born anew' (born of the Spirit) 'That which is born of the Spirit is spirit.' John 3:6
So it's not just water but water and the Spirit. We are baptized in his name to have our sins blotted out, and we are born of the Spirit. Jesus was born of the Spirit. How can he be the first of those born of the Spirit if we are not born of the Spirit as he was?
Justin Martyr:
"As many as are persuaded and believe that what we [Christians] teach and say is true, and undertake to be able to live accordingly, and instructed to pray and to entreat God with fasting, for the remission of their sins that are past, we pray and fast with them. Then they are brought by us where there is water and are regenerated in the same manner in which we were ourselves regenerated. For, in the name of God, the Father . . . and of our Savior Jesus Christ, and of the Holy Spirit [Matt. 28:19], they then receive the washing with water. For Christ also said, ‘Unless you are born again, you shall not enter into the kingdom of heaven’ [John 3:3]" (First Apology 61 [A.D. 151]).
First of all we fast 'to loose the bonds of wickedness' and we do it by 'sharing our bread with the hungry and bringing the homeless poor into our house'. Then the LORD will 'answer when we call' Isa. 58:6-9 I would disagree with Justin that we fast for the remission of sin but I agree with him about fasting and prayer. We fast to be heard by God. I think we are washed for the remission of sin.